document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1193886>Question 1193886</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Read the following hypothetical case and answer the questions below.<BR>\n" );
document.write( "The Indiana Inc. a lead denim manufacturer in New Orleans has productions<BR>\n" );
document.write( "sites in four different counties with production ratio at 8:5:3:4. Their key products<BR>\n" );
document.write( "are skinny jeans (50%), straight leg jeans (35%) and jeggings (15%). Each of<BR>\n" );
document.write( "these products come in two styles  -  stone washed (60%) and plain (40%). Their<BR>\n" );
document.write( "monthly production cost is about $0.95 mn. All products in both styles are<BR>\n" );
document.write( "produced at all the four sites, while the manufacture proportion is maintained<BR>\n" );
document.write( "across the production sites.<BR>\n" );
document.write( "1. The analysts at Indiana Inc intend to draw a sample for a quick analysis.<BR>\n" );
document.write( "Propose a probability sampling technique elucidating the steps clearly.\r<BR>\n" );
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document.write( "2. The following table shows the sale price for each product:<BR>\n" );
document.write( "Sales Prices Skinny Jeans Straight Leg<BR>\n" );
document.write( "Jeans Jeggings<BR>\n" );
document.write( "Stone Washed $210 $185 $170<BR>\n" );
document.write( "Plain $185 $90 $110<BR>\n" );
document.write( "3) Given that 5,000 units were produced last month what is the revenue<BR>\n" );
document.write( "generated for each product line? Comment about the status of business at<BR>\n" );
document.write( "Indiana Inc.\r<BR>\n" );
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document.write( "4)If it is known that the product is stone washed jeans what are the chances<BR>\n" );
document.write( "that it is skinny jeans?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848551 by </B><A HREF=/tutors/aboutme.mpl?userid=parmen><B>parmen(42)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=parmen><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=848551\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> **1. Probability Sampling Technique**\r<BR>\n" );
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document.write( "**Stratified Sampling**\r<BR>\n" );
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document.write( "* **Steps:**<BR>\n" );
document.write( "    1. **Divide the population into strata:** In this case, the production sites in the four counties can be considered strata. <BR>\n" );
document.write( "    2. **Determine the sample size for each stratum:** Allocate the sample size to each stratum proportionally to its size within the population. Since the production ratio is 8:5:3:4, allocate samples to each county in this proportion. <BR>\n" );
document.write( "    3. **Randomly select units within each stratum:** Use a random number generator or a table of random numbers to select the required number of units (e.g., jeans) from each county's production.\r<BR>\n" );
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document.write( "**Advantages of Stratified Sampling:**\r<BR>\n" );
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document.write( "* Ensures representation from each production site.<BR>\n" );
document.write( "* Improves the accuracy of the sample by reducing sampling error.<BR>\n" );
document.write( "* Allows for analysis of differences between production sites.\r<BR>\n" );
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document.write( "**2. Revenue Generated for Each Product Line**\r<BR>\n" );
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document.write( "* **Calculate the number of units produced for each product:**<BR>\n" );
document.write( "    * Skinny Jeans: 5000 units * 50% = 2500 units<BR>\n" );
document.write( "    * Straight Leg Jeans: 5000 units * 35% = 1750 units<BR>\n" );
document.write( "    * Jeggings: 5000 units * 15% = 750 units\r<BR>\n" );
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document.write( "* **Calculate revenue for each product and style:**<BR>\n" );
document.write( "    * **Skinny Jeans:**<BR>\n" );
document.write( "        * Stone Washed: 2500 units * 60% * $210 = $315,000<BR>\n" );
document.write( "        * Plain: 2500 units * 40% * $185 = $185,000<BR>\n" );
document.write( "    * **Straight Leg Jeans:**<BR>\n" );
document.write( "        * Stone Washed: 1750 units * 60% * $185 = $194,250<BR>\n" );
document.write( "        * Plain: 1750 units * 40% * $90 = $63,000<BR>\n" );
document.write( "    * **Jeggings:**<BR>\n" );
document.write( "        * Stone Washed: 750 units * 60% * $170 = $76,500<BR>\n" );
document.write( "        * Plain: 750 units * 40% * $110 = $33,000\r<BR>\n" );
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document.write( "* **Total Revenue:** $315,000 + $185,000 + $194,250 + $63,000 + $76,500 + $33,000 = $866,750\r<BR>\n" );
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document.write( "**Comment on Business Status:**\r<BR>\n" );
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document.write( "* Based on the revenue figures, Indiana Inc. appears to be generating significant revenue. <BR>\n" );
document.write( "* Skinny jeans and stone-washed jeans are the highest-revenue generators. <BR>\n" );
document.write( "* Further analysis would be needed to assess profitability, market share, and competitive landscape to fully evaluate the business status.\r<BR>\n" );
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document.write( "**3. Probability of Skinny Jeans given Stone Washed**\r<BR>\n" );
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document.write( "* **Let:**<BR>\n" );
document.write( "    * A: Event that the product is Skinny Jeans<BR>\n" );
document.write( "    * B: Event that the product is Stone Washed\r<BR>\n" );
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document.write( "* **Given:**<BR>\n" );
document.write( "    * P(A) = Probability of Skinny Jeans = 50% = 0.5<BR>\n" );
document.write( "    * P(B) = Probability of Stone Washed = 60% = 0.6<BR>\n" );
document.write( "    * P(A and B) = Probability of Skinny Jeans and Stone Washed = 0.5 * 0.6 = 0.3\r<BR>\n" );
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document.write( "* **Use Bayes' Theorem:**<BR>\n" );
document.write( "    * P(A | B) = P(B | A) * P(A) / P(B)<BR>\n" );
document.write( "    * P(A | B) = (P(A and B) / P(A)) * P(A) / P(B)<BR>\n" );
document.write( "    * P(A | B) = P(A and B) / P(B) <BR>\n" );
document.write( "    * P(A | B) = 0.3 / 0.6 = 0.5\r<BR>\n" );
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document.write( "* **Therefore, the probability that the product is Skinny Jeans given that it is Stone Washed is 0.5 or 50%.**\r<BR>\n" );
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document.write( "I hope this comprehensive analysis is helpful!<BR>\n" );
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